Segment Proofs Vocab

What is the Reflexive Property of Congruence?

• Any geometric figure is congruent to itself. Example: AB ≅ AB.

• Two geometric figures are congruent if they have the same area.

• The sum of the angles in a triangle is always 180 degrees.

• If two angles are congruent, their corresponding sides are also congruent.

What is the definition of a ray?

• A ray is a part of a line that starts at an endpoint and extends infinitely in one direction.

• A ray is a line that has two endpoints and does not extend infinitely.

• A ray is a part of a circle that extends from the center to the circumference.

• A ray is a straight line that connects two points without any endpoints.

What does it mean for a point to be a midpoint?

• A midpoint divides a segment into two equal parts. If L is the midpoint of TJ, then TL = LJ.

• A midpoint is the point that is farthest from both endpoints of a segment.

• A midpoint is the point that divides a segment into three equal parts.

• A midpoint is the point that is closest to one endpoint of a segment.

What is the definition of congruent segments?

• Segments that have the same length are called congruent segments.

• Segments that are parallel to each other are called congruent segments.

• Segments that intersect at a right angle are called congruent segments.

• Segments that are of different lengths are called congruent segments.

What is the Division Property of Equality?

• If a = b and c ≠ 0, then a/c = b/c.

• If a + b = c, then a = c - b.

• If a = b, then a + c = b + c.

• If a * b = c, then a = c / b.

What is the Transitive Property of Congruence?

• If figure A is congruent to figure B and figure B is congruent to figure C, then figure A is congruent to figure C.

• If figure A is congruent to figure B, then figure B is not congruent to figure A.

• If figure A is not congruent to figure B, then figure A is congruent to figure C.

• If figure A is congruent to figure B and figure C is congruent to figure D, then figure A is congruent to figure D.

What is the Addition Property of Equality?

• If a = b, then a + c = b + c. Example: If 2x - 5 = 10, then adding 5 to both sides gives 2x = 15.

• If a = b, then a - c = b - c. Example: If 2x + 3 = 10, then subtracting 3 from both sides gives 2x = 7.

• If a = b, then a * c = b * c. Example: If 2x = 10, then multiplying both sides by 2 gives 4x = 20.

• If a = b, then a / c = b / c. Example: If 2x = 10, then dividing both sides by 2 gives x = 5.

What is the Transitive Property?

• If a = b and b = c, then a = c.

• If a + b = c, then a = c - b.

• If a > b and b > c, then a > c.

• If a * b = c, then a = c / b.

What is the Substitution Property?

• If a = b, then b can be substituted for a in any expression. Example: If x = 3, then 2x = 6 can be rewritten as 2(3) = 6.

• If a = b, then a can be substituted for b in any expression. Example: If x = 3, then 2x = 6 can be rewritten as 2(2) = 6.

• If a = b, then a and b are equal but cannot be substituted in expressions.

• If a = b, then a + c = b + c for any value of c.

What is the Symmetric Property of Congruence?

• If figure A is congruent to figure B, then figure B is congruent to figure A. Example: If AB ≅ CD, then CD ≅ AB.

• If figure A is congruent to figure B, then figure A is not congruent to figure B.

• If figure A is not congruent to figure B, then figure B is congruent to figure A.

• If figure A is congruent to figure B, then figure C is congruent to figure A.